In a conventional fuel injector for internal combustion engines (described, for example, in German Patent Application No. DE 102 57 895 A1), the fluid-carrying pipe is integrated into the valve housing and runs at a parallel offset with respect to the housing axis, the pipe connecting the intake nipple to the valve chamber upstream from the valve seat in the nozzle body remote from the intake nipple. The valve housing encloses a cavity which has a circular-cylindrical cross-section, inside which cavity a piezoelectric or magnetorestrictive actuator is disposed for actuating the valve. The housing wall, which has a circular ring-shaped cross-section, is radially built up on one side throughout its length and provided with an axial bore in the built-up region, in which the pipe is guided. At the lower end, the pipe is bent at approximately 90°, inserted in a radial opening in the nozzle body discharging into the valve chamber and welded or soldered to the nozzle body. At the end facing away from the nozzle body, the pipe is affixed to the intake nipple and permanently connected to the intake nipple.